Abstract. CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time con...
The barycenter heuristic is often used to solve the NP-hard two-layer edge crossing minimization problem. It is well-known that the barycenter heuristic can give solutions as bad a...
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from diffe...